344 THE SCIENCE OF LOGIC 



establishing. Hence, the proofs found in all the &quot; exact,&quot; or 

 &quot; abstract,&quot; or &quot; mathematical &quot; sciences, run in the mood Bar 

 bara, (d) It is the most natural form of reasoning, inasmuch as 

 the extremes suffer no inversion, occupying in the premisses the 

 same position, as subject and predicate, which they occupy in 

 the conclusion ; whereas in the second figure the major extreme, 

 in the third the minor extreme, and in the fourth (or first indirect) 

 both extremes, suffer inversion of position in the passage from 

 premisses to conclusion. 



The Dictum de omni et nullo is directly applicable to this figure alone. 

 The only difference between Barbara and Darit, and between Celarent and 

 Ferio, is that in the two universal moods the principle laid down in the major 

 is definitely applicable to all the members of the class 5, whereas in the 

 particular moods the extent of its application is left indefinite. And the only 

 difference between the two affirmative and the two negative moods is that in 

 the former case the general principle or law laid down is affirmative, while in 

 the latter it is negative. 



Dr. Keynes sums up the four moods in the following scheme : ] 



&quot; Rule . . . All M is P (or is not P), 



Case . . . All (or some) S is M, 



Result . . . therefore, All (or some) S is P (or is not /*).&quot; 



With this it will be interesting to compare the mixed hypothetical syl 

 logism (179) : 



&quot; If anything is M it is P (or is not /&amp;gt;), 



Certain subjects, 5, are M y 

 therefore, They are P (or are not P)&quot; &quot; 



This presentation of the first figure is practically the same as Kant s 

 analysis of the syllogism : an analysis which he applied to hypothetical and 

 disjunctive, as well as to categorical, syllogisms. The major premiss he 

 interpreted as a rule connecting a predicate (/*, P) with a condition (M}, the 

 minor premiss as a subsumption of a subject fulfilling this condition, and the 

 conclusion a determination of this subject by the predicate of the rule. The 

 canon or axiom of the syllogism thus interpreted would be : &quot; Whatever 

 satisfies the condition of a rule falls under the rule &quot;. 8 



171. CHARACTERISTICS OF THE SECOND FIGURE. The 

 second figure (a) proves only negatives. Hence it is appropriate 

 for the &quot; discovery or proof of the distinctions between things,&quot; 4 

 or for the disproof of some positive assertion, (b) It has been 

 called the Exclusive Figure, because by means of it we may go 

 on successively disproving or eliminating a number of supposi- 



1 op. cit., p. 336, with other symbols. -ibid., n. 2. 



3 Cf. JOSEPH, op. cit., p. 286. 



4 LAMBERT, Neues Organon, ii., p. 139. C/. JOSEPH, op. cit., p. 192 : &quot; The con 

 clusion states a fact of difference between two things, which the premisses prove 

 hut do not account for&quot;. 



